Use Newton's method to estimate the requested solution of the equation. Start with given value of X0 and then give x2 as the est imated solution. x3 + 5x +2 = 0; x0 = -1; Find the one real solution.
1 answer:
Answer:
<h2>
-0.3913 </h2>
Step-by-step explanation:
Given the initial value of X0 = -1, we can determine the solution of the equation x³ + 5x +2 = 0 using the Newton's method. According to newton's approximation formula;
If
We will iterate using the formula;
Given f(x) = x³ + 5x +2
f(x0) = f(-1) = (-1)³ + 5(-1) +2
f(-1) = -1 -5 +2
f(-1) = -4
f'(x) = 3x²+5
f'(-1) = 3(-1)²+5
f'(-1) = 8
f(-0.5) = (-0.5)³ + 5(-0.5) +2
f(-0.5) = -0.125-2.5+2
f(-0.5) = -0.625
f'(-0.5) = 3(-0.5)²+5
f'(-0.5) = 3(0.25)+5
f'(-0.5) = 0.75+5
f'(-0.5) = 5.75
The estimated solution is -0.3913 (to 4dp)
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